We numerically investigate pressure-driven, density-unstable displacement flows of two miscible fluids along a near-horizontal 2D channel. The displacing fluid is a Newtonian fluid, slightly heavier than the displaced yield stress (Bingham) fluid. The imposed displacement flow is laminar. We show that the displacement flow is mainly governed by five dimensionless numbers, and their combinations, including the Reynolds number (Re), the Bingham number (Bn), the densimetric Froude number (Fr), the viscosity ratio (m), and the channel inclination angle (beta). In this work, we primarily focus on the viscosity ratio and provide a detailed understanding of the flow behaviours via studying the effects of m on displacement flow patterns, regime classifications based on slump-type and centre-type displacement flow regimes, leading and trailing displacement front features, and finally the effects of m at different inclination angles.